Many NMR experiments require frequency selective radio frequency (rf) pulses and a variety of schemes have been developed for this purpose. Most of the commonly used methods involve controlling pulse widths and interpulse delay times between a collection of constant amplitude rectangular rf pulses. For example, the soft pulse and the Dante pulse scheme have been used to selectively suppress intense solvent peaks and to obtain the spectra of solutes dissolved in water.
In experiments where selective excitation of resonances located in a narrow range of the spectrum is required, the soft pulse and the Dante pulse schemes have again been used. However, in both cases there are undesirable features arising from lobes that are present on either side of the central excitation frequency. These lobes may result in the excitation of undesired resonances. While these excitations of undesired resonances are not large for small tip angles, they are quite severe for larger tip angles such as 90.degree..
The soft pulse is generated by using a relatively long, low amplitude pulse (as compared to the short, high-amplitude pulse used to generate a hard pulse) to gate on/off an rf carrier. The resulting soft pulse has the Fourier spectrum of the sinc function. Methods used in generating the hard and soft pulse have the virtue that they only involve relatively simple on-off gating of the rf carrier at a predetermined amplitude during the pulse duration.
However, it is known that improved selectivity in frequency excitation results when the excitation pulse is modulated by a frequency function of the sinc or Gaussian form. This required more complex circuitry to develop the modulator of these functions on a carrier frequency.
One such solution to the problem of generating a selective rf pulse is to use a computer to control the time-dependent amplitude of an rf pulse or collection of pulses in a manner that leads to the appropriate distribution in frequency. In this approach, the Fourier transform of the desired rf spectral distribution is calculated, stored in a computer memory, and then fed into a mixer to modulate the amplitude of the carrier frequency with the calculated time dependent function. In addition, predetermined correction factors are used to modify the calculated functions stored in the computer memory so as to correct for nonlinearities in the rf mixers and amplifiers. By computing the appropriate functional form, which is then stored in the computer, any excitation pattern could in principle be devised.
This is strictly true only for small tip angles of the magnetization vector, since the spin system then responds linearly to the excitation pulse.
One example of a computer-controlled method in generating rf excitation signals that have the exact spectral characteristics is by amplitude and frequency modulation of the rf carrier. This technique uses modulating functions generated by synthesizers and waveform generators. A disadvantage to this technique is that additional equipment not usually found on commercial spectrometers is required.
It is, therefore, an object of the invention to provide a new and improved apparatus and method for generating modulating functions for a pulsed rf carrier.
It is yet another object of the present invention to use defined filter functions of relatively inexpensive filters, instead of a computer to generate the rf carrier modulating function.